1. Technical Field
The present invention relates to a motion analyzing apparatus.
2. Related Art
In various fields, apparatuses that analyze the motion of a person or an object are necessary. For example, by analyzing the swing trajectory of a tennis racket or a golf club, the form of baseball pitching or batting, and the like and clarifying points to be improved based on the analysis result, game power can be improved.
Currently, as practical motion analyzing apparatuses, apparatuses that analyze a motion by consecutively photographing a measurement object, to which a mark is attached, using an infrared camera or the like and calculating the motion trajectory of the mark using consecutive photographed images are generally used.
JP-A-2004-24488 is an example of the related art.
However, in such apparatuses, since an infrared camera used for photographing images is necessary, the size of the apparatuses is in consequence large, and, accordingly, there is a problem in that it is difficult to handle the apparatuses. For example, in a case where the images of a tennis practice are desired to be acquired through photographing at a plurality of angles, it is necessary to move the position of the infrared camera or change the direction of a player in accordance with the desired photographing angles.
In contrast to this, recently, an apparatus was proposed which analyzes the motion of a measurement object based on output data of a small inertial sensor by installing the inertial sensor in the measurement object. Such an apparatus does not need an infrared camera, and accordingly there is an advantage of easy handling. For example, the velocity v(t) and the position p(t) of the measurement object can be calculated by performing a time integration process as shown in the following Equations (1) and (2) for an acceleration value a(t) detected by an acceleration sensor.
                              v          ⁡                      (            T            )                          =                                            ⁢                              a                ⁡                                  (                  t                  )                                            ⁢                              ⅆ                t                                      +                          v              0                                                          (        1        )                                                                                    p                ⁡                                  (                  T                  )                                            =                                                                    ∫                    0                    T                                    ⁢                                                            v                      ⁡                                              (                        t                        )                                                              ⁢                                          ⅆ                      t                                                                      +                                  p                  0                                                                                                        =                                                                    ∫                    0                    T                                    ⁢                                                            ∫                      0                      T                                        ⁢                                                                  a                        ⁡                                                  (                          τ                          )                                                                    ⁢                                              ⅆ                        τ                                            ⁢                                              ⅆ                        t                                                                                            +                                                      v                    0                                    ⁢                  T                                +                                  p                  0                                                                                        (        2        )            
However, generally, an error other than a value to be observed is included in the output value of an inertial sensor. Accordingly, for example, the output data x(t) of the acceleration sensor can be represented as the following Equation (3) by using an acceleration value a(t) and an error ε(t).x(t)=a(t)+ε(t)  (3)
Accordingly, in a case where the velocity v(t) and the position p(t) of a measurement object are calculated by performing a time integration process as represented in the following Equations (4) and (5) based on the output data x(t) of the acceleration sensor, the error ε(t) is integrated with respect to time as well. Therefore errors in the velocity v(t) and the position p(t) rapidly increase in accordance with the elapse of time t.
                                          ∫            0            t                    ⁢                                    x              ⁡                              (                t                )                                      ⁢                                                  ⁢                          ⅆ              t                                      =                              v            ⁡                          (              T              )                                +                                    ∫              0              τ                        ⁢                                          ɛ                ⁡                                  (                  t                  )                                            ⁢                                                          ⁢                              ⅆ                t                                              +                      c            1                                              (        4        )                                                      ∫            0            τ                    ⁢                                    ∫              0              t                        ⁢                                          x                ⁡                                  (                  τ                  )                                            ⁢                              ⅆ                τ                            ⁢                                                          ⁢                              ⅆ                t                                                    =                              p            ⁡                          (              T              )                                +                                    ∫              0              τ                        ⁢                                          ∫                0                t                            ⁢                                                ɛ                  ⁡                                      (                    τ                    )                                                  ⁢                                                                  ⁢                                  ⅆ                  τ                                ⁢                                  ⅆ                  t                                                              +                                    c              1                        ⁢            T                    +                      c            2                                              (        5        )            
In other words, in a motion analyzing apparatus using an inertial sensor, the characteristics of the sensor are not sufficient in practice, and in a case where the posture, the velocity, the position, and the like are calculated by performing an integration process for the output data of the inertial sensor, an error included in the output of the sensor noticeably increases through the integration process, whereby there is problem in that a sufficient analysis (measurement) capability is not acquired.